The short distance behavior of (φ 4)3

Brydges, David C.; Dimock, J.; Hurd, T. R.

doi:10.1007/bf02104514

Cited by 39 publications

(39 citation statements)

References 18 publications

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“…Our treatment of the RG map on polymer activities is similar to that used in previous papers [13], [15], [5], [6]. However there are essential modifications: references [5], [6], which we follow as much as possible, use open polymers while we have to use closed polymers as in [13], [15] (see the discussion in the next section ). Our norms are now simpler as well, a simplification we pay for with some harder proofs.…”

Section: Estimates On the Rg Mapmentioning

confidence: 99%

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Sine-Gordon Revisited

Dimock

Hurd²

2000

Ann. Henri Poincaré

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We study the sine-Gordon model in two dimensional space time in two different domains. For β > 8π and weak coupling, we introduce an ultraviolet cutoff and study the infrared behavior. A renormalization group analysis shows that the the model is asymptotically free in the infrared. For β < 8π and weak coupling, we introduce an infrared cutoff and study the ultraviolet behavior. A renormalization group analysis shows that the model is asymptotically free in the ultraviolet.

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Section: Estimates On the Rg Mapmentioning

confidence: 99%

“…Proof: A computation shows that V n (∆, φ) ≤ 1 and the first bound follows. For the second bound we compute the n th derivative and resum as in [5] and find (2h) n n! (e ζV (∆) ) n (φ) ≤ exp ∞ n=0 (2h) n n!…”

Section: A Appendixmentioning

confidence: 99%

Sine-Gordon Revisited

Dimock

Hurd²

2000

Ann. Henri Poincaré

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“…While equivalent to the Gallavotti-Nicolò [8,9,10] method, the continuous RGE is much simpler technically. An application of continuous RG methods to nonperturbative bosonic problems [11,12] requires many new ideas and a combination with cluster expansion techniques, to control the combinatorics. It is one of the points of this paper that for fermions, the straightforward adaption of the method yields a determinant bound which improves the combinatorics of fermionic theories as compared to bosonic ones, and may lead to nonperturbative bounds.…”

Section: Introductionmentioning

confidence: 99%

Continuous Renormalization for Fermions and Fermi Liquid Theory

Salmhofer¹

1998

Communications in Mathematical Physics

136

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I derive a Wick ordered continuous renormalization group equation for fermion systems and show that a determinant bound applies directly to this equation. This removes factorials in the recursive equation for the Green functions, and thus improves the combinatorial behaviour. The form of the equation is also ideal for the investigation of manyfermion systems, where the propagator is singular on a surface. For these systems, I define a criterion for Fermi liquid behaviour which applies at positive temperatures. As a first step towards establishing such behaviour in d ≥ 2, I prove basic regularity properties of the interacting Fermi surface to all orders in a skeleton expansion. The proof is a considerable simplification of previous ones. 0

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“…More specificly many multi-scale approaches (see [2,5,6,8]) use an inductive description of a sequence of effective actions on different momentum or length scales which are generated by renormalization group transformations. An additional inductive procedure is then applied to obtain the correlation functions.…”

Section: Academic Pressmentioning

confidence: 99%